TurboCAD Parabola

TC Parabola first created 19/09/05 last modified 21/09/05- Page Author: Ty Harness

Richard Williams Project - Creating parabolic curves with TurboCAD - unfinished work

Aims:

Make TurboCAD draw parabolas and paraboloids using VBA macros to make it easy and fun

To understand the nature of parabolas

Real world examples and the use of parabolas

Please see More on parabolas

Menaechmus[1] is credited with the discovery of the curves known as the ellipse, parabola, and the hyperbola.

Figure 1 - Creating a paraboloid with TurboCAD

Figure 2 - TurboCad screen shot

Copy and paste the code below into the VBA module

Private Const degtorad = 0.017453292
Private Const PI = 3.141592654





Sub parabola()


Dim x As Double, y As Double
Dim diameter As Double

diameter = 3
Dim a As Double 'focal point height
a = 0.4

Dim radius As Double

radius = diameter * 0.5

Dim grs As Graphics
Dim gr1 As Graphic


Set grs = ActiveDrawing.Graphics
Set gr1 = grs.Add(, "polyline")
 
x = -radius


For t = -100 To 100
x = x + radius / 100
y = a * x ^ 2
Set ver = gr1.Vertices.Add(x, y, 0)
Set ver = Nothing
Next t



'ActiveDrawing.Graphics.AddLineSingle -diameter * 0.5, 0, 0, diameter * 0.5, 0, 0

ActiveDrawing.Graphics.AddLineSingle 0, -a, 0, 0, y, 0

ActiveDrawing.Graphics.AddLineSingle -diameter * 0.5, a, 0, diameter * 0.5, a, 0
ActiveDrawing.Graphics.AddText "F", 0, a, 0, a

ActiveDrawing.Graphics.AddLineSingle -diameter * 0.5, -a, 0, diameter * 0.5, -a, 0
ActiveDrawing.Graphics.AddText "directrix", 0, -a, 0, a

   

Set gr1 = Nothing

ActiveDrawing.ActiveView.ZoomToExtents

End Sub



Sub paraboloid()

Dim x As Double, y As Double, thick As Double

Dim grs As Graphics
Dim gr As Graphic
Dim gr1 As Graphic



Set grs = ActiveDrawing.Graphics
Set gr1 = grs.Add(, "polyline")


Set gr = grs.Add(, "TCW40SPIN")  '
    gr.Properties("$ROTATIONANGLE") = 360 'deg
     
   'axis of rotation

   Set ver = gr.Vertices.Add(0, 0, 0)
   Set ver = Nothing
   Set ver = gr.Vertices.Add(0, 100, 0)
   Set ver = Nothing


Dim diameter As Double
diameter = 3
Dim a As Double 'focal point height

a = 0.4

Dim radius As Double
radius = diameter * 0.5


 
x = 0

For t = 0 To 51
y = a * x ^ 2
Set ver = gr1.Vertices.Add(x, y, 0)

Set ver = Nothing
x = x + radius / 50
Next t


thick = 0.05

For t = 51 To 0 Step -1
x = x - radius / 50
y = a * x ^ 2
theta = 2 * a * x
xp = x + thick * Sin(theta)
yp = y - thick * Cos(theta)

If xp <= 0 Then
Exit For
End If
Set ver = gr1.Vertices.Add(xp, yp, 0)

Set ver = Nothing


Next t

Set ver = gr1.Vertices.AddClose
Set ver = Nothing

 Set gr1 = grs.Remove(gr1.Index)
    gr.Graphics.AddGraphic gr1

Set gr1 = Nothing
Set gr = Nothing


ActiveDrawing.ActiveView.ZoomToExtents




End Sub

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References

[1] Boyer, C.B., A History of Mathematics, Wiley(1989), 93.